After coming back from the holidays, you found out
that you gained weight. You are now going on a diet
using IIFYM. You must eat 100g of protein, 60g of
fat, and 250g of carb a day. Twix is $2 and has
10g of carb and 1g of fat. Oatmeal is $5 and has 5g
of carb and 3g of protein. Egg is $3 and has 10g of
protein and 5g of fat. Lastly, Big Mac is $5 and has
10g of everything.
What is the least expensive way to fill your macro?

This problem can be solved using linear programming (LP) to minimize the cost of fulfilling the macronutrient requirements while taking into account the contribution of each food item to carbs, protein, and fats. The goal is to determine how many Twix bars, Oatmeal servings, Eggs, and Big Macs you should consume to hit the macro targets while minimizing costs.

### Define the variables:
- Let $ x_1 $ be the number of Twix bars.
- Let $ x_2 $ be the number of servings of Oatmeal.
- Let $ x_3 $ be the number of Eggs.
- Let $ x_4 $ be the number of Big Macs.

### Objective:
Minimize the cost of buying these foods. The total cost function can be written as:
\[
\text{Minimize} \, C = 2x_1 + 5x_2 + 3x_3 + 5x_4
\]

### Constraints:

1. **Protein requirement (100g of protein):**
\[
3x_2 + 10x_3 + 10x_4 \geq 100
\]
(Oatmeal contributes 3g, Eggs contribute 10g, and Big Macs contribute 10g of protein.)

2. **Fat requirement (60g of fat):**
\[
1x_1 + 5x_3 + 10x_4 \geq 60
\]
(Twix contributes 1g, Eggs contribute 5g, and Big Macs contribute 10g of fat.)

3. **Carb requirement (250g of carbs):**
\[
10x_1 + 5x_2 + 10x_4 \geq 250
\]
(Twix contributes 10g, Oatmeal contributes 5g, and Big Macs contribute 10g of carbs.)

4. **Non-negative variables**: 
All variables $ x_1, x_2, x_3, x_4 \geq 0 $.

We can now use a linear programming solver to minimize the cost subject to these constraints. Let me calculate the solution.The least expensive way to meet your macronutrient goals is as follows:

- **15 Twix bars** 
- **10 Big Macs**
- **0 Oatmeal servings**
- **0 Eggs**

The total cost for this combination is **$80**.

This combination ensures you hit the required macronutrient goals for protein, fats, and carbohydrates while minimizing the cost.

Would you like more details or have any questions? Here are 5 related questions that might interest you:

1. What happens if the cost of Twix or Big Macs changes?
2. How do different diet constraints affect the solution?
3. What if you need a more balanced intake between the food items?
4. How can you modify this method for personal taste preferences?
5. What if certain food items are unavailable or have a limited quantity?

**Tip:** When optimizing for diet, consider not just the macros but also micronutrients and variety to maintain overall health!

After coming back from the holidays, you found out that you gained weight. You are now going on a diet using IIFYM. You must eat 100g of protein, 60g of fat, and 250g of carb a day. Twix is $2 and has 10g of carb and 1g of fat. Oatmeal is $5 and has 5g of carb and 3g of protein. Egg is $3 and has 10g of protein and 5g of fat. Lastly, Big Mac is $5 and has 10g of everything. What is the least expensive way to fill your macro?

Find the least expensive way to meet your macronutrient goals for protein, fats, and carbohydrates using linear programming. This example solves the IIFYM diet optimization problem, featuring cost minimization while satisfying daily macro requirements. Suitable for advanced math students.

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